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AMSC 698K Description and Prerequisites

Course Description

AMSC 698K, Topics in Kinetic Theory This is the first semester of a two-semester sequence designed to survey current understanding of the justification of fluid dynamics from kinetic theory. After a brief review of classical mechanics, various theories of fluid dynamics will be intorduced from a traditional continuum perspective. The classical Boltzmann equation will then be introduced followed by other kinetic theories. Fluid dynamic regimes will be identified, and various fluid dynamical systems will be derived. Moment closure recipes will be used to derive moment systems for transition regimes. Applications to rarefied gases, semiconductor modeling, radiative transport, and plasmas will be given. This semester will have a formal and physical emphasis, while the second will be more mathematical. A tentative outline for the entire year is given below.

Course Prerequisites

This course is intended for both students in mathematics and students in applied fields. Students should have some knowledge of partial differential equations (PDE), either directly or through courses such as fluid mechanics, quantum mechanics, or semiconductor design that use PDE extensively. Some knowledge of classical mechanics or thermodynamics would also be helpful, but is not necessary. Please feel free to contact me concerning your background if you have any questions.

More Details

There will be no exams. Each student will be expected to produce two written reports on somes of the lectures.

Tentative Outline of First Term

Part 1: Preliminaries

Part 2: Kinetic Theories

Part 3: Fluid Dynamical Approximations and Beyond

Rough Tentative Outline of Second Term

Part 4: Mathematical Theories for Fluids

Part 5: Mathematical Theories for Kinetic Models

Part 6: Mathematical Theories for Fluid Dynamical Limits